0=-2t^2-10t+9

Solution for 0=-2t^2-10t+9 equation:

0=-2t^2-10t+9

We move all terms to the left:

0-(-2t^2-10t+9)=0

We add all the numbers together, and all the variables

-(-2t^2-10t+9)=0

We get rid of parentheses

2t^2+10t-9=0

a = 2; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·2·(-9)
Δ = 172
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{43}}{2*2}=\frac{-10-2\sqrt{43}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{43}}{2*2}=\frac{-10+2\sqrt{43}}{4}
$